Rose chooses R1 every time. Colin chooses C2 or C2.
The game equilibrium equals 10. However, it is not a pure strategy Nash Equilibrium since Colin can choose either C2 or C3 and get the same result.
Pitcher chooses knuckleball every time, it is a dominant strategy. The Batter must subsequently guess knuckleball each time.
The pure strategy Nash equilibrium equals 0.250.
Linear Program for Rose
Linear Program for Colin
library(lpSolve)
payoff.matrix <- as.matrix(rbind(
c(3000, 4500, 6000),
c(1000, 9000, 2000),
c(4500, 4000, 3500)))
Maximin = 20, Minimax = 15, therefore no pure strategy staddle point exists.
Colin plays C1 or C2 Rose plays R1 Game value: 10
First, check for pure strategy saddle point:
One exists at C1, R2 and equals 0.6.